Question

Solving a compound linear inequality

Answer 1

(-5, -2)

Explanation:

Given inequalities:

`4w+3 > -17`

`3w-6 < -12`

Solve each inequality.

`\begin{aligned}\implies 4w+3 & > -17\\4w & > -20\\w& > -5\end{aligned}`

`\begin{aligned}\implies 3w-6 & < -12\\3w& < -6\\w& < -2\end{aligned}`

Therefore, combining the solutions gives:

`-5 < w < -2`

Therefore, the solution to the compound inequality in interval notation is (-5, -2).